Temperature measurement in semiconductor devices such as integrated circuits on silicon substrates is often done by taking advantage of the fundamental relationship between the saturation current of a p-n junction and its temperature. This relationship is described by the Diode Equation shown below:I=IS*[exp(qV/nkT)−1]where,                Is=saturation current        q=electron charge        V=p-n junction voltage        n=ideality factor (between 1 and 2)        k=Boltzmann's constant        T=absolute temperature (K)        
The ideality factor n is equal to 2 for pure recombination current (low voltage, low current density), and equal to 1 for pure diffusion current (higher voltages).
When using a p-n junction as a temperature sensor, it is desirable that n be close to 1. However, high current densities should be avoided to minimize ohmic effects due to series resistances outside of the p-n junction. Ohmic effects can lead to a deviation from the Diode Equation.
FIG. 1 shows a conventional thermal sensor 100. A current source 105 with a single diode 110 is used, with sequential measurements being taken for current and voltage to obtain two I-V data pairs (I1, V1) and (I2, V2) for the diode 110. The temperature T is then calculated (neglecting the −1) from the Diode Equation as follows:T=(q/nk)*(V2−V1)/(ln(I2/I1))
The (−1) term in the Diode Equation may be ignored since the resulting error is usually less than 1 part in 100,000 for all current densities of interest.
In conventional temperature measurements made using a single diode, there are a number of error sources that reduce the accuracy and reliability of the measurements. Also, the sequential measurements reduce the frequency with which measurements can be made.
In the measurement of the two voltages, the error associated with each individual measurement contributes to the total error for the term (V2−V1). Since this term is normally quite small (about one tenth of V2 or V1), the accuracy of the voltage measurements is critical. Also, voltage measurements usually involve an analog-to-digital conversion, with an associated quantization error that is counted twice.
Another source of error are leakage currents. For example, shunt resistance 120 may produce a deviation from the I-V characteristic expressed by the Diode Equation. Also, since the measurements are sequential, short term changes in the circuit state can affect the measurements. As previously described, a series resistance 115 may also introduce error.